Which power allows the president to influence laws after passing through Congress?

The power that allows the president to influence laws after they have passed through Congress is the power to veto bills. When Congress passes a bill, it is sent to the president for approval. If the president disagrees with the bill or certain aspects of it, they can exercise their veto power, which effectively prevents the bill from becoming law unless Congress overrides the veto with a two-thirds majority in both the House of Representatives and the Senate.

This power is significant because it acts as a check on Congress, ensuring that the president has a mechanism to reject legislation they deem unfit. This influence can serve as a powerful negotiating tool, encouraging lawmakers to consider the president's preferences during the legislative process, as they may wish to avoid the possibility of a veto. The veto power thus plays a crucial role in the balance of power between the legislative and executive branches of government.

In contrast, the power to sign bills into law constitutes direct approval but does not allow for any influence after the fact. The power to appoint federal judges influences the judiciary but does not pertain to specific legislation. Similarly, the power to issue pardons does not relate to the legislative process and focuses instead on individual cases in the criminal justice system.